Unemployment in the eurozone hit a fresh high in November after the jobless rate jumped to 11.8%, illustrating the difficulties faced by officials in Brussels seeking to show the bloc is on the mend.

The news came as Ireland's deputy prime minister warned that Britain's possible exit from the European Union is now the "big challenge" facing Europe.

Official figures from Eurostat showed that the number of unemployed in the struggling 17 member currency union jumped to 18.8 million. Across the wider European Union, the unemployment total hit 26 million for the first time out of a working population of almost 230 million. The unemployment rate for the 27 member EU remained at 10.7%, the same as in October, but up from 10% a year ago.

The European commission president, José Manuel Barroso, argued in an upbeat speech on Monday that the currency union had put the worst behind it and no longer faced an existential crisis – but Tuesday's unemployment data laid bare the continued discrepancies between different nations.

The unemployment situation is particularly dire in southern European countries where the situation has become entrenched, especially among the under 25s. Youth unemployment in Italy rose to an all-time high above 37% in November, while Greece and Spain registered rates above 50%.

Economists have forecast unemployment will keep rising. Tom Rogers, senior economic adviser at Ernst & Young, said he expected the rate to hit 12.5% by early 2014 "as eurozone businesses and households remain wary and governments continue to cut back".

Laszlo Andor, the EU's employment commissioner, warned that record unemployment and fraying welfare systems in southern Europe risk creating a new divide in the continent.

"A new divide is emerging between countries that seem trapped in a downward spiral of falling output, fast rising unemployment and eroding disposable incomes and those that have so far shown good or at least some resilience," he said.

Last year had been "another very bad year for Europe in terms of unemployment and the deteriorating social situation," said Andor.

The biggest rise in unemployment over the past year took place in Greece, where joblessness soared to 26% in September, up 7.1 percentage points over September 2011's 18.9%. But the highest overall rate in the EU was in Spain, where 26.6% of the workforce was jobless in November.

Austria, however, posted the lowest unemployment rate in the EU, at 4.5%. The rate in Germany was 5.4%, with 7.8% in Britain and 10.5% in France.

Meanwhile, Ireland's deputy prime minister, Eamon Gilmore, criticised David Cameron's idea of renegotiating the UK's relationship with Brussels. Speaking at an event to mark the start of Ireland's presidency of the European Union, Gilmore said: "This is not going to work if we have 27 different categories of membership." He added that Britain leaving the EU, a scenario dubbed "brexit", had replaced Greece leaving the euro as the continent's biggest potential challenge.